Entropy Balancing in High Dimensions

Apoorva Lal

Minimal working example of Double-LASSO augmented entropy balancing estimator proposed in Lal (2021).

rm(list = ls())
library(LalRUtils)
set.seed(42)
# paths
source("estimators.R")

##       wants        loaded
##  [1,] "tidyverse"  TRUE  
##  [2,] "data.table" TRUE  
##  [3,] "hdm"        TRUE  
##  [4,] "ebal"       TRUE  
##  [5,] "glue"       TRUE  
##  [6,] "rlist"      TRUE  
##  [7,] "lfe"        TRUE  
##  [8,] "janitor"    TRUE  
##  [9,] "caret"      TRUE  
## [10,] "kosel"      TRUE

experimental benchmark (Lalonde 86)

library(causalsens)
data(lalonde.exp)
summary(robustify(felm(re78 ~ treat, lalonde.exp)))$coefficients[2, 1:2]

##   Estimate Std. Error 
##     1794.3      670.8

Implementation on PSID Lalonde Sample

Estimation akin to Dehejia & Wahba (1999).

Traditional Estimators

data(lalonde.psid)
dtpsid = data.table(lalonde.psid)
y = 're78'
w =  'treat'
x = setdiff(colnames(lalonde.psid), c(y, w))
# %% traditional estimators
dm_est  = diffmeans(dtpsid, y, w)
cov_est = covaradjust(dtpsid, y, w, x)
ipw_est = ipw_reg(dtpsid, y, w, x)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

eb_est = eb_reg(dtpsid, y, w, x)
lr_est = rbind(dm_est, cov_est, ipw_est, eb_est)
rownames(lr_est) = c('difference in means', 'regression', 'ipw', 'entropy balancing')

Double LASSO and Knockoff EB

y = 're78'
w =  'treat'
x = setdiff(colnames(lalonde.psid), c(y, w))
# %% basis expansion and interaction creation step
data = prep_matrices('re78', 'treat', controls = x, dat = dtpsid)
y = data[[1]]
w = data[[2]]
X = data[[3]]

# %% estimation using double lasso, and knockoff lasso + knockoff-ebal
hdres = estimate_hdc(y, w, X)

final estimates

rbind(lr_est, hdres)

##                     Estimate Std. Error
## difference in means   -15205      655.9
## regression             -8746     3720.6
## ipw                   -14501     1132.9
## entropy balancing       2425      876.5
## Partial-Out            -1553     1141.1
## Double Selection       -1651      938.3
## Knockoff Selector      -3717      916.7
## Knockoff EB             2302      945.3

Knockoff-EB comes closest to the experimental benchmark. All the regression estimators (and IPW) estimate the wrong sign.